Question 121413
In polynomial function equations, complex roots always occur in conjugate pairs.  
So if (1-2i) is a solution, so is (1+2i).
The simplest form, g(x), would then be,
{{{g(x)=(x-(1-2i))(x-(1+2i))(x-(-3))}}}
{{{g(x)=(x-1+2i)(x-1-2i)(x+3)}}}
{{{g(x)=(x^2-2x+5)(x+3)}}}
{{{g(x)=(x^3-2x^2+5x)+(3x^2-6x+15)}}}
{{{g(x)=x^3+x^2-x+15}}}